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Magnetism and Matter - Solutions (Level 0)
Student Name: ____________________________________ Class: 12 Subject: Physics
Topic 1: The Bar Magnet
Part I: Fill in the Blanks
1.
The SI unit of magnetic dipole moment is ________.
Solution: Ampere-meter squared ($\text{A m}^2$ or $\text{J/T}$).
2.
Outside a bar magnet, magnetic field lines run from the ________ pole to the ________ pole.
Solution: North, South.
3.
Inside a bar magnet, magnetic field lines run from the ________ pole to the ________ pole.
Solution: South, North. (Forming continuous closed loops).
4.
A freely suspended bar magnet aligns itself in the roughly ________ direction.
Solution: North-South.
5.
The formula for magnetic potential energy of a dipole in a uniform magnetic field is $U =$ ________.
Solution: $-\vec{m} \cdot \vec{B}$ (or $-mB \cos\theta$).
Part II: Multiple Choice Questions (MCQs)
6.
The torque on a magnetic dipole $\vec{m}$ in a uniform magnetic field $\vec{B}$ is:
Solution: (b) $\vec{m} \times \vec{B}$
7.
At which angle is a magnetic dipole in stable equilibrium in a magnetic field?
Solution: (a) $0^\circ$ (Minimum potential energy, $U = -mB$).
8.
Two magnetic field lines:
Solution: (c) Never intersect (Otherwise there would be two directions of magnetic field at the point of intersection).
9.
A current-carrying solenoid behaves like a:
Solution: (c) Bar magnet (Produces identical exterior magnetic field lines).
10.
Magnetic dipole moment is a:
Solution: (b) Vector quantity (Directed from South to North pole).
Part III: True or False
11.
The magnetic length of a bar magnet is slightly less than its geometric length.
Solution: True (Magnetic length $\approx$ $5/6$ of geometric length because poles reside slightly inside).
12.
Work done in rotating a dipole from angle $\theta_1$ to $\theta_2$ is $mB(\cos\theta_1 - \cos\theta_2)$.
Solution: True ($W = \int_{\theta_1}^{\theta_2} mB\sin\theta d\theta$).
Part IV: Match the Following
13.
Match the physical quantities in Column A with their formulas in Column B:
Solution:
(P) Torque ($\tau$) $\rightarrow$ (2) $mB\sin\theta$
(Q) Potential Energy ($U$) $\rightarrow$ (3) $-mB\cos\theta$
(R) Magnetic Moment of coil $\rightarrow$ (1) $NIA$
Topic 2: Gauss's Law in Magnetism
Part I: Fill in the Blanks
14.
According to Gauss's law for magnetism, the net magnetic flux through any closed surface is ________.
Solution: Zero.
15.
The mathematical expression for Gauss's law in magnetism is $\oint \vec{B} \cdot d\vec{S} =$ ________.
Solution: $0$.
16.
Gauss's law in magnetism indicates that isolated magnetic ________ do not exist.
Solution: Monopoles.
Part II: Multiple Choice Questions (MCQs)
17.
Which of the following is strictly true for magnetic lines of force?
Solution: (a) They form continuous closed loops.
18.
The absence of magnetic monopoles means:
Solution: (c) $\oint \vec{B} \cdot d\vec{S} = 0$ (Net flux out of any volume is zero).
19.
If a bar magnet is cut into two equal halves transversely (perpendicular to its length), we get:
Solution: (b) Two smaller, complete dipoles.
20.
If an electric dipole is enclosed in a Gaussian surface, the net electric flux is zero. If a magnetic dipole is enclosed, the net magnetic flux is:
Solution: (c) Zero.
Part III: True or False
21.
The net magnetic flux through a sphere containing a bar magnet is positive.
Solution: False (It is strictly zero).
22.
Magnetic poles always exist in equal and opposite pairs.
Solution: True.
Topic 3: Earth's Magnetism
Part I: Fill in the Blanks
23.
The angle between the geographic meridian and the magnetic meridian at a place is called magnetic ________.
Solution: Declination.
24.
The angle made by the Earth's total magnetic field $\vec{B}$ with the horizontal direction is called angle of ________.
Solution: Dip (or Inclination).
25.
At the magnetic equator, the angle of dip is ________.
Solution: $0^\circ$ (Zero).
26.
At the magnetic poles, the angle of dip is ________.
Solution: $90^\circ$.
27.
The horizontal component of Earth's magnetic field is $B_H =$ ________.
Solution: $B \cos I$ (where $I$ is angle of dip).
Part II: Multiple Choice Questions (MCQs)
28.
The vertical component of Earth's magnetic field $B_V$ is given by:
Solution: (a) $B \sin I$
29.
The relation between total magnetic field $B$, horizontal component $B_H$, and vertical component $B_V$ is:
Solution: (b) $B^2 = B_H^2 + B_V^2$ (Pythagoras theorem).
30.
If $B_H = B_V$ at a specific place, the angle of dip at that place is:
Solution: (c) $45^\circ$ ($\tan I = B_V / B_H = 1$).
31.
A dip circle shows an angle of $90^\circ$ when placed at the:
Solution: (c) Magnetic poles (Field is purely vertical).
32.
The Earth's magnetic field at the surface is approximately of the order of:
Solution: (a) $10^{-4} \text{ Tesla}$ (1 Gauss).
Part III: True or False
33.
Magnetic declination is constant and remains the same at all places on Earth.
Solution: False (It varies from place to place).
34.
A compass needle points exactly along the geographic north pole everywhere on Earth.
Solution: False (It points to the magnetic north pole, which is offset from the geographic north).
Part IV: Match the Following
35.
Match the Earth's magnetic parameters:
Solution:
(P) Angle of Dip at Magnetic Equator $\rightarrow$ (2) $0^\circ$
(Q) Angle of Dip at Magnetic Poles $\rightarrow$ (3) $90^\circ$
(R) Ratio of $B_V / B_H$ $\rightarrow$ (1) $\tan I$
Topic 4: Classification of Magnetic Materials
Part I: Fill in the Blanks
36.
Materials that are feebly repelled by a strong magnet are called ________ materials.
Solution: Diamagnetic.
37.
Materials that are strongly attracted by a magnet are called ________ materials.
Solution: Ferromagnetic.
38.
The magnetic susceptibility ($\chi$) of a diamagnetic substance is small and ________ (positive/negative).
Solution: Negative.
39.
Above the ________ temperature, a ferromagnetic substance transitions and behaves like a paramagnetic material.
Solution: Curie.
40.
Relative permeability ($\mu_r$) for a ferromagnetic material is ________ (very large / very small).
Solution: Very large ($\mu_r \gg 1$).
Part II: Multiple Choice Questions (MCQs)
41.
Which of the following is a diamagnetic material?
Solution: (c) Copper.
42.
Which of the following is a classic example of a ferromagnetic material?
Solution: (b) Iron.
43.
The magnetic susceptibility ($\chi$) of a paramagnetic material is:
Solution: (c) Small and positive.
44.
When a diamagnetic substance is brought near the north or south pole of a strong bar magnet, it is:
Solution: (b) Repelled.
45.
For a paramagnetic material, the relative permeability ($\mu_r$) is:
Solution: (c) $\mu_r > 1$ (slightly).
Part III: True or False
46.
Diamagnetism is a universal property present in all atomic materials.
Solution: True (Though it may be masked by stronger paramagnetic or ferromagnetic effects).
47.
Curie's law states that the magnetization of a paramagnetic material is directly proportional to its absolute temperature.
Solution: False (It is *inversely* proportional to absolute temperature).
Part IV: Match the Following
48.
Match the material with its susceptibility ($\chi$):
Solution:
(P) Diamagnetic $\rightarrow$ (2) Small negative ($-1 < \chi < 0$)
(Q) Paramagnetic $\rightarrow$ (3) Small positive ($\chi > 0$)
(R) Ferromagnetic $\rightarrow$ (1) Large positive ($\chi \gg 1$)
Topic 5: Hysteresis, Permanent Magnets & Electromagnets
Part I: Fill in the Blanks
49.
The phenomenon of lagging of magnetic induction ($B$) behind the magnetizing field ($H$) is called ________.
Solution: Hysteresis.
50.
The value of magnetization left in a ferromagnetic material when the external magnetizing field is reduced to zero is called ________.
Solution: Retentivity.
51.
The reverse magnetizing field required to completely demagnetize a material ($B=0$) is called ________.
Solution: Coercivity.
52.
Electromagnets should have high permeability and ________ (high/low) retentivity.
Solution: Low (So they demagnetize quickly when current is turned off).
53.
Materials used for making permanent magnets should have high retentivity and ________ (high/low) coercivity.
Solution: High (So they are not easily demagnetized by stray fields).
Part II: Multiple Choice Questions (MCQs)
54.
Soft iron is preferred for making cores of electromagnets and transformers because it has:
Solution: (c) High permeability, low hysteresis loss.
55.
The area enclosed by the hysteresis loop ($B-H$ curve) represents:
Solution: (c) Energy dissipated per cycle per unit volume.
56.
Steel is preferred over soft iron for making permanent magnets because of its:
Solution: (b) High coercivity (Harder to demagnetize).
57.
A ferromagnetic substance with a very narrow hysteresis loop is suitable for:
Solution: (b) Making transformer cores (To minimize AC heating/energy loss).
58.
What happens to a ferromagnetic substance if it is heated beyond its Curie temperature?
Solution: (c) It becomes paramagnetic.
Part III: True or False
59.
Coercivity is a measure of how easily a magnetic material can be demagnetized.
Solution: True (High coercivity means it is difficult to demagnetize).
60.
Energy is dissipated in the form of heat during each complete cycle of magnetization and demagnetization.
Solution: True (This is called Hysteresis Loss).